Physicists have put a new twist on the
humble corkscrew. Just as a butterfly
appears identical to its mirror image,
objects made of structures that tilt,
twist or spiral possess a symmetry now
recognized for the first time. The discovery is based on a mathematical operation
that transforms a clockwise helix into a
counterclockwise one, or vice versa.

“Normally, a helix flips when you put
a mirror up to it,” says Venkatraman
Gopalan, a materials scientist at Penn
State University in University Park.
“We’ve developed a special kind of mirror

with this math woven into
it.” Seen in this mirror, an
object with a spiral shape
will look just like itself.

This symmetry joins a
list of other, long-known
ways to move or manipulate an object and leave
it looking the same afterward. A snowflake has
what’s called rotational
symmetry: Turn it 60
degrees, and its appearance doesn’t change. A piece of wallpaper
with a repeating pattern looks identical
when moved a bit to the right or left,
demonstrating translational symmetry.

“This new symmetry we’re playing
around with has not been taken into
account up to now,” says Daniel Litvin,
a physicist at Penn State Berks in Read-ing who along with Gopalan reported the
results in the April 3 Nature Materials.

During the late 19th century, scientists figured out
that symmetries limit the
number of ways atoms can
be arranged into crystals,
calculating 230 possible
patterns. In the mid-20th
century another kind of
symmetry, time reversal,
extended the number of
possible arrangements
in magnetic materials to
1,421. With Gopalan and
Litvin’s ne w “rotation-reversal” symmetry, crystallographers now have 17,807
patterns to look for when trying to characterize a material’s 3-D structure.

“People have looked at certain materials and wondered why they have certain
properties,” says Manfred Fiebig, a physicist at the University of Bonn in Germany.
“Now they may be able to argue that it’s
because of this new symmetry.”